Stability and Hopf bifurcation analysis of fractional‐order nonlinear financial system with time delay

Abstract

We deal with a fractional‐order nonlinear financial model with time delay in this paper. The quantitative analysis of the model has been done in which the asymptotic stability of the equilibrium points of the model have been discussed. Furthermore, the Hopf bifurcation analysis of the model has been done under the impact of time delay. The stability of the model has been studied with the reproduction number less than or greater than 1. The analysis of the model has been done by using the Laplace transformation technique. The analysis shows that the fractional‐order model with a time delay can adequately enhance the elements and fortify the results for either stable or unstable criteria. All unstable cases in the nonlinear financial system are converted to stable cases for fractional order under neighborhood points. The reproduction ranges of all parameters have been discussed. The paper examines the impact of time delay and the importance of determining essential parameters such as saving amount by using Hopf bifurcation. Finally, numerical simulations have been carried out by MATLAB to illustrate our derived results. The financial system is verified under the theoretical outcomes from parameter estimation.